What is the leading coefficient of -6x^4 + 7x^3 - x + 9?

• A. -6
• B. 7
• C. -1
• D. 9

Answer: (A)

The leading coefficient is the coefficient of the term with the highest power of x when the polynomial is written in descending powers. In -6x^4 + 7x^3 - x + 9, the highest power is x^4, and its coefficient is -6, so the leading coefficient is -6. The other terms have lower powers (x^3, x, and the constant 9), so they don’t affect the leading coefficient. The negative leading coefficient also tells you the ends of the graph go downward as x → ±∞.